AERO3260 AERODYNAMICS 1 LECTURE NOTES

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1 AERO3260 AERODYNAMICS 1 LECTURE NOTES

2 Contents Potential flow formulas... 7 Introduction... 8 What will we study?... 8 Challenges:... 8 Assignments :... 8 Resources:... 8 Current assignment:... 9 Aerofoil features... 9 Air mach numbers... 9 Introduction:... 9 Wing section:... 9 Why Aerofoils work Wing section types: Aerofoil with camber NACA Aerofoil Effects of wing section: Writing reports Lab report Components: Structure Components: Aerofoils (again) Stall Factors that contribute to stall Reducing stall abruptness: Leading edge stall Trailing edge stall Selecting an aerofoil Maximising lift Increasing lift High lift devices Supercritical aerofoils Naviar Stokes and Potential Flow theory Equations of motion: Naviar stokes equation Derivation: Continuity equation

3 Naviar stokes equation Potential flow Point vortex Complex potential: Stream: Source Vortex D aerofoil theory Introduction Modelling wing section Conformal mapping Joukowski transformation Lifting flat plate (transforming spinning circular cylinder) Vortices (tute) Thick aerofoils Leading and trailing edge Circulation around thick aerofoils Introducing camber: Karman treffits aerofoil Generalised Karman Treffitz conformal map Theodorsen aerofoil design The ζ plane: (aerofoil) Theodorsen aerofoil design Thin aerofoil theory Camber line Uncambered aerofoil Cambered aerofoils Comparison of 2D aerofoil theories: Tute: thin aerofoil theory D panel method Panel placement Problem statement: Higher order accuracy than panel method: Viscous inviscid interaction: EIF construction Solving: Method 1:

4 Solving: Method 2: Design of aerofoils: Optimisation techniques: Optimisation theory: Evolutionary algorithms: Some objective functions: PARSEC Method: Inverse design methods: Potential flow in 3D: Wind tunnel experiments and measurements Introduction: Types of aerodynamics experiments: Wind tunnel principles: Scale parameters: Open circuit wind tunnels: Closed circuit wind tunnel Advantages/disadvantages: Wind tunnel dimensions: Test section: Vanes: Corner loss coefficient: Vane design: Fans: Purpose of the Fan: Fan section: Honeycomb: Screens: Contraction cone: Contraction design: Cooling of wind tunnels: Cooling methods: Flow quality: Steadiness: Turbulence: Special kinds of tunnels: Transonic tunnels:

5 Supersonic tunnels: Hypersonic tunnels: Icing tunnels: Automotive tunnels: Water tunnels: Energy of a tunnel: Energy ratio Loss around tunnel: Close circuit tunnel losses (generally) Instrumentation testing and procedure: Introduction: Working section airspeed: Instruments: Flow visualisation: Aerodynamic load measurements: Pressure distribution measurements: Experimental error: Common sense errors: Wind tunnel correction: D FLOW End plates D flow: D flow basics: Flow streamlines: Wingtip vortices: D aerodynamic feedback loop: Modelling of flow around 3D wings Vortex filament and tubes: Simplified Lift distribution: Horseshoe vortex: D flow field: Elliptical lift distribution: Induced drag: General loading equation Aerodynamics of General wing planforms: Vortex Lattice method:

6 Practical Aerodynamics: Calculating CD Interference factor Q CD0 components Accounting for interference: Supervelocities: Notes on CD Delta Wing Flow: Slender Wings Boundary Layer Theory Naviar stokes assumptions: continuity x momentum Y momentum: Historical context: Benjamin Robbins Fluid dynamic drag: History of Viscosity: Boundary Layer Theory: Naviar Stokes in 2D: Boundary Conditions: No slip condition Wall shear: Force on a plate: Pressure gradient: Boundary layer in 3D: Solution of Boundary Layer Equations Blasius Flow: Separation: Orr-Sommerfield equation en method Von Karman momentum integral Boundary Layer Solutions: Solutions: Assumed profile: Pohlausen Polynomial Solution

7 Thwaites Method: For aerofoils: Blasius wall shear stress

8 AERO3260 AERODYNAMICS 1 LECTURE NOTES Gareth VIo Lecture 1. Tuesday, 26 July 2016 Potential flow formulas name velocity Stream function Potential function Uniform (Cartesian) (U, 0,0) ψ = Uy φ = Ux Uniform (cylindrical) u = (0,0, U) ψ = 1 φ = Ux 2 UR2 Simple source (spherical) Dipole souirce M 4π ( S 4πr 2, 0,0) cos θ (2 r 3, S S ψ = cos θ φ = 4π 4πr sin θ r 3, 0) ψ = M sin2 θ 4πr M r r 4πr 2 Line source u r e r Sθ S ln r 2π 2π Line dipole ( εs πr 2 cos θ, εs εs sin θ, 0) sin θ πr2 πr εs cos θ πr Stagnation point (Ax, Ay, 0) Axy 1 2 A(x2 y 2 ) Axisummetric 1 stagnation point Line vortex (polar) ( 1 2 Ar, 0, Az) 1 2 AR2 z Γ (0, 2πr ) Γ Γ ln r 2π 4 A(R2 2z 2 ) 2π θ 7

9 Introduction - Viscocity o Stall o Dynaic stall o Separation o Laminar/turbulent flow o Pressure gradients What will we study? - Potential flow theory (incompressible) o 2D building blocks; learng to analyse aerofoil properties o Its extension to 3D - Wind tunnel theory - Boundary layer theory o Estimate viscous drag - Aerofoil behaviour o Geometric properties - Compressibility effects - Intro to CFD o Terminology. Solutions. Pit falls, advantages Challenges: - incompressible aerodynamics is lots of maths - What we see mathematically is very simplified; and lost physical reality. Assignments : 3 assignments (5,10,10) released weeks 1,5,10 (last is group) 3 labs (5,`10,5) - Week 2/3 cylinder flow - Week 5/6 2D aerofoil flow - Week 10/11 3D flow o Reports due one week after lab session Weekly submission of exercise (5) Exam (50%) (need 40% in exam) Resources: - Anderson; fundementals of aerodynamics - Abbott: theory of wing sections - Kuethe; foundations of aerodyanamics - Bertin; aerodynamics for engineers - Doug s aerodynamics for students 8

10 Current assignment: - Page limit - 2 parts o Part A: requies you to solve a problem (which aerofoil to use) - Part B o Research and literature survey - Submission 2PM Thursday week 4 - Intermediate submission with penalty applied (week 2 and 3) Lecture 2. Thursday, 28 July 2016 Assignment: just assume unitary span; only have lift and weight forces L unit span = 1 2 ρu2 (chord)c L Aerofoil features Air mach numbers Subsonic M < 1 Supersonic M > 1 Sonic M = 1 Hypersonic M > 5 Transonic 0.75 < M < 1.2 Introduction: - Most important phenomenon in a wind tunnel studied is flow around wing - Several major improvements in aircraft aerodynamics have resulted from the study of new forms of wing sections o (make sure you know temp and pressure for wind tunnel experiments) Wing section: Wing section is a 2D cut out of a wing. - Its shape is crucial to the aerodynamic performance of the wing o o o Lift curve; dc l = 2π (need to remember this idealisation) dα Drag curve Moment curve; dc l dα = 1.8π ( t max c ) 9

α is the angle of attack 2D flow uses lower case c l, c d ; 3D flow upper case C L ; C D Why Aerofoils work Bernoulli: longer travel time on top surface (incorrect) Newton: air hitting lower surface

11 α is the angle of attack 2D flow uses lower case c l, c d ; 3D flow upper case C L ; C D Why Aerofoils work Bernoulli: longer travel time on top surface (incorrect) Newton: air hitting lower surface of wing and reaction force ; assuming that α is important to Newton: 1. In order for the aerofoil to go up, air must go down (true) 2. So angle of attack is important (top plays no part) (half true) Bernoulli: 1. Air is redirected up on top of wing (true) 2. Air travels further on top (true; not relevant) 3. Air must come back to meet bottom surface at same time (FALSE) 4. Therefore air on top is faster (true, not for given reason) 5. By Bernoulli s equation, faster air on top exerts less pressure (true, not for given reason) Reality: Need both to explain Air is forced down (downwasg) due to a speeding up of air on the top of the wing; (Bernoulli effect phenomenon) The effect is so pronounced that air passing over the wing passes around wing faster that those on bottom. - Calculation shows that positive pressure on the bottom of wing is insufficient for the entire explanation - It is negative pressure on top of the wing which accounts for most lift Downwash is strongest near body of plane and weakest at wingtips. Effect produces vortices in the downwash. 10

Boundary layer Most of flow field does not be effected by wing; Only thin boundary layer; if we assume boundary layer is not there we can get a reasonable approximation of lift, but drag is non

12 Boundary layer Most of flow field does not be effected by wing; Only thin boundary layer; if we assume boundary layer is not there we can get a reasonable approximation of lift, but drag is non existent (as no viscosity) C D = C D0 + kc L 2 Wing section types: Different section types fro different applications; the correct type must be chosen, and is then used to create wing s geometry 11

13 Modern airlines have aerofoil changing from the root to the tip. Re = ρuc μ 12

14 Aerofoil with camber 13

15 Types of camber Zero camber (symmetric) Positive camber (lift up) Negative camber (lift down) Thickness distribution x u = x y t sin θ y u = y c + y t cos θ x l = x + y t sin θ y l = y c y t sin θ 14

16 General aerofoil specifications: Low speed Hobby aircraft, UAV Less than Re Selif, Lissaman famous Subsonic: Large leading edge nose radius Performance invariant to small AoA change No major drag sacrifice Max mach 0.75/0.8 Transonic Maximisation of drag divergence mach number dc d dm = 0.1 Supersonic 1 < M < 5 mach number Reduce wave drag Small thickness (3.36% for F104) Natural laminar aerofoil: (First used in P51) - Lower skin drag - Minimum pressure point as far downstream as possible - Manage pressure gradient - External disturbances (Tollmien-Schlichting waves (instability)) Multi element - High lift increased weight increased cost - Single, double and triple element (each increasing in weight and cost) - But about 0.1 increase in c l is roughly 1 less in angle in approach, so we don t need as big a landing gear Morphing - Change shape - Alternative to multi element NACA Aerofoil NACA 4 series: - Ground breaking as it parametrised the aerofoil The geometry equation is: y t = a 0 x a 1 x a 2 x 2 + a 3 x 3 a 4 x 4 - The square root helps with the leading edge nose radius: 15

17 R LE = [1 + ( dt 2 dx ) ] d 2 t dx t max NACA2412; max camber = 2%; location from leading edge= 4 ; maximum thickness t = 12% 10 - Issues with camber line, extreme values of camber, extreme forward camber locations NACA 5 series: NACA last 2 digits are thichness as a percentage of the chord. The others are parametrised as coefficients NACA 6 series: NACA k 1 6 (x3 3mx 2 + m 2 (3 m)x) y C = C(( k 1 m 3 ) (1 x) 6-1 st digit indicated 6 series - 2 nd is the chordwise position of the minimum pressure in 1/10 of the chord for symmetrical aerofoil at c l = 0 Effects of wing section: = angle of zero lift - Lift curve slope - Max lift - Angle of max lift - Moment around the ¼ Tute 1 16

18 Writing reports - Simplicity and clarity - Write a few drafts Lab report Components: - Abstract - Introduction - Methods - Results - Discussion - Conclusion Structure Title page Abstract/summary Intro Methodology Findings/results Analysis Summary/conclusion References Appendices - Write shorthand to sound scientific/objective - Facts and details rather than analysis - Imply analysis and reasoning without making argument explicit - Assume reader will read meaning into text - Good usage, spelling, grammar and punctuation Components: Intro: background/objectives, scope and limits, previous work/research; important background information, research aims, (how does lab fit in with body of work) Method: procedure/material Results: data, tables, figures, calculations Discussion: link to intro, interpretation, alternative explanations Conclusion: summary main point References: sources 17

19 Where to start: Start with data, not intro How to display the data to be meaningful and concise Trends in figures Connect results analysis to theory Theory: - Which research question did you set out to answer - Expected answer or assumptions o Hypothesis o Designed to prove Methods: Results - Accurate and complete account of method - Present data - State in verbal as well as visual - Draw attention to key points - Number/title tables/graphs - Appendix for raw data or complex calculations Conclusion: - Short and to the point - State what you know - No new information should be disclosed - Tie into the introduction Cover page: - Neat and clean - Typed - Make a good impression - Include o Title of lab o Name, SID; lab parternes o Date Technical writing language: - Impersonal; avoid first person 18

Common mistakes - Don t rewrite lab sheet o There are many plotters which do a better job o If using matlab, don t put a grey background - Don t use default excel style plots (find better ones) -

20 Common mistakes - Don t rewrite lab sheet o There are many plotters which do a better job o If using matlab, don t put a grey background - Don t use default excel style plots (find better ones) - Write meaningful figure captions - Computer spell checks can t recognise gibberish - Don t print table and graph. Graph has information, put table in the appendix - Negative drag is not a thing!!! - Incorrect referencing: reference has to appear in the text otherwise it s a bibliography - Error analysis (should contain error analysis) o Sources of errors not listed (realistic errors) o Error bars in results (X and Y) - Plots o Include units, labels o Make possible to read o Discrete points o How to connect the points - No referencing of figures/tables in text - Don t see as seen in figure below, say in figure 3 - Reference figures/data from external sights (or it s plagiarism) - Comparison to literature o Not evident o Severely lacking o Not mentioning who comparing with - Work on english Lecture 3. Tuesday, 2 August 2016 Aerofoils (again) L = 1 2 ρu2 SC l = ρuγ Leading edge nose radius - Small leading edge radius has sharp stall break - Large leading edge radius has gentle stall break Stall 19

Increasing angle of attack too much creates separation; so not enough lift created (stall) Factors that contribute to stall As angle of attack increases the stagnation point moves further down on the

21 Increasing angle of attack too much creates separation; so not enough lift created (stall) Factors that contribute to stall As angle of attack increases the stagnation point moves further down on the forward part of the aerofoil; making a longer effective upper surface - This creates friction that increases with travel distance - Pressure gradient (pressure change) o Decrease in pressure from leading edge, which decreases with distance o This decreasing pressure tends to induce the flow to move along the surface, promoting the flow direction we want (favourable pressure gradient) accelerating decelerating Beyond this peak in negative pressure we find a reversal As angle of attack increases the centre of pressure moves forward and unfavourable pressure gradient becomes longer and steeper - Eventually, the combined effect of the unfavourable pressure gradient and the surface friction becomes greater than the energy available in the airflow - With not flow over top surface, there is no mechanicsm to reduce pressure and lift decreases o Lift does not go to zero; just a big drag penalty 20

22 Reducing stall abruptness: - Roundess of leading edge acts as a barrier to flow at high angle of attack - Stall stripes Leading edge stall Linear increase in cl until stall At α just below 15º streamlines are highly curved (large lift) and still attached to upper surface of aerofoil At α just above 15º massive flow-field separation occurs over top surface of aerofoil significant loss of lift Called Leading Edge Stall Characteristic of relatively thin aerofoils with thickness between about 10 and 16 percent chord 21

23 Trailing edge stall Progressive and gradual movement of separation from trailing edge toward leading edge as α is increased Thin aerofoil stall - Flow separates even at very small α - Initially small regions of flow separate to form separation bubble - As increased reattachment point moves further downstream until total separation Bubble increases the camber; which changes the Cl alpha curve 22

24 Surface oil visualisation Lecture 4. Thursday, 4 August 2016 Selecting an aerofoil - Highest maximum lift coefficient - Proper ideal or design lift coefficient - Lowest c d - Highesft L/D ratio - Highest lift curve slope - Lowest pitching moment coeff - Proper stall quality - Can be structurally reinforced - Must be able to be manufactures - Cost 23

25 - Other design requirements - Integration of aerofoils along span Maximising lift - 2 parameters critical and both dictated by pressure distribution o Boundary layer separation o Onset of supersonic flow - Upper surface is most critical - Try and achieve constant pressure across top surface - Reduce shock strength and wave drag Increasing lift Take off and landing needs to be augmented L = 1 2 ρu2 S dc L dα α - We have the ability to change U and S 24

26 High lift devices 25

27 Common ones are - Simple flap o Increase camber and angle - Fowler flap o Increase camber, angle of incidence and wing area - Nose flap o Increase camber Slats Reduce velocity over upper side of main wing and increases on the lower side - Severity of adverse pressure gradient reduced - Lower pressure on upper side is offset by higher pressure on lower side Flaps Increase velocity over both surfaces - Increase speed help again negative pressure gradient - Effective angle of attack is increased - Extra circulation created for kutta condition 26

28 27

29 Supercritical aerofoils Slotted - Reenergise the BL - Negative camber ahead of slot - Large amount of positive camber after slot - Increase in skin friction - Extremely sensitive to sape - Keeps flow constant over upper surface to avoid negative pressure gradient - Reduce shock strength - Delay drag rise 28

30 29

31 Standard vs supercritical aerofoil 30

32 In supersonic flow, there can also be internal shockwaves inside the flow 31

33 Effect of thickness at trailing edge Naviar Stokes and Potential Flow theory Equations of motion: Naviar stokes equation - Most complete model of flow in a continuum is NS - Only a model - Represents 3 conservations law: mass, momentum and energy - There are models starting from the Boltzmann equation Derivation: Look at infitesimal fluid element; with velocity u, v, w and length dx, dy, dz Mass (continuity): 32

34 - Net mass flow rate is rate of change of mas per time Momentum: Energy: - Rate of increase in momentum + rate at which momentum leaves = body forces+pressure force+viscous force - Rate of change of energy = flux of heat +rate of work Stress tensor: Continuity equation Naviar stokes equation Tensor notation: ρ t + (ρv ) = 0 ρ Du i Dt = ρ x i + μ 2 u i x i 2 Vector notation: ρ ( u t u u + ( u ) u ) = p + μ 2 u Matrix notaiotn: ρ ( u t + T u u T ) = p + μ 2 u Comments: - Most compete form of airflow equation although turbulence not explicity defined - Explicit definition of turbulence further complicates the equation by introducing new unkowns, the Reynolds stressed - The most famous models for turbulence are the kω; kε and wall model - No explicit solution - Equations are: unsteady, non linear, viscous, compressimble (nonliearity is big problem) 33

35 Constant viscosity equations: Incompressible Steady euler equations Incompressible: u = 0; steady: t = 0 μ constant assumption u u = 1 ρ p u = 0 - Easier to solve than naviar stokes; but still requires numerical methods (eg finite difference). Very few analytical solutions (and only for specific cases) Flow rotation Without viscocity; we can t apply shear to a little section, so infinitesimal section is irrotational Irrotational flow u = 0 - Some flows can be idealised as irrotational - In general, attaches, incompressible, inviscid flow is also irrotational - The curl of the velocity is zero Potential flow Irrotationality leads to the simultaneous equations: v x u y = 0 34

Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.

Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular